Make sure it's really text. If you copy from another browser, word processor, e-mail, then it's likely represented on the clipboard as HTML and RTF, along with "plain text". Do a "cleanse" by pasting into Notepad, then re-copying FROM Notepad, and then see if it pastes. If it does, then the problem is with the heavy-weight formats.
The other thing that makes me wonder... when you say "paste a large material on my site", what does that mean, really? You're pasting into a text box? What happens next, it's inserted into a database via PHP or something? It really isn't clear what you're doing here.